The problem presents a sequence of words and asks to find the missing term. We need to identify the pattern or rule governing the transformation from one word to the next in the sequence.
C) VENTUR — Based on the identified pattern of alternately removing the first and last letter, the term after DVENTUR is obtained by removing the first letter 'D', resulting in VENTUR.
The problem presents a series of letters and asks us to find the missing letter. This type of problem typically involves identifying a pattern in the alphabetical positions or the differences between consecutive letters.
Correct Option: D) S is the missing letter because the differences between consecutive letters are increasing by 1 (3, 4, 5, 6, 7).
This problem involves concepts of work and time, specifically dealing with efficiency. We are given the time taken by one person to complete a task and the relative efficiency of another person. We need to find the time taken by the second person. The key idea is that efficiency is inversely proportional to the time taken to complete a certain amount of work.
Determine Sakshi's efficiency:
If Sakshi can do a piece of work in 20 days, her efficiency (work done per day) can be represented as:
\[ \text{Sakshi's efficiency} = \frac{1}{\text{Time taken by Sakshi}} = \frac{1}{20} \text{ work/day} \]Calculate Tanya's efficiency:
Tanya is 25% more efficient than Sakshi. This means Tanya's efficiency is Sakshi's efficiency plus 25% of Sakshi's efficiency.
\[ \text{Tanya's efficiency} = \text{Sakshi's efficiency} + 0.25 \times \text{Sakshi's efficiency} \] \[ \text{Tanya's efficiency} = \text{Sakshi's efficiency} \times (1 + 0.25) \] \[ \text{Tanya's efficiency} = \text{Sakshi's efficiency} \times 1.25 \]Substitute Sakshi's efficiency:
\[ \text{Tanya's efficiency} = \frac{1}{20} \times 1.25 \] \[ \text{Tanya's efficiency} = \frac{1.25}{20} = \frac{125}{2000} = \frac{5}{80} = \frac{1}{16} \text{ work/day} \]Calculate the number of days taken by Tanya:
The number of days taken to complete the work is the reciprocal of the efficiency.
\[ \text{Days taken by Tanya} = \frac{1}{\text{Tanya's efficiency}} \] \[ \text{Days taken by Tanya} = \frac{1}{\frac{1}{16}} = 16 \text{ days} \]Correct Option: B) 16
Tanya is 25% more efficient than Sakshi. Since efficiency and time are inversely proportional, Tanya will take less time than Sakshi. Specifically, if Sakshi takes 20 days, Tanya will take \(20 / 1.25 = 16\) days.
The question asks for the term that describes the increase in atmospheric temperature caused by carbon dioxide. This phenomenon is a fundamental concept in environmental science and climate change.
B) Greenhouse effect — The greenhouse effect is a natural process that warms the Earth's surface. When the Sun's energy reaches Earth's atmosphere, some of it is reflected back to space and the rest is absorbed and re-radiated by greenhouse gases, including carbon dioxide, methane, and water vapor. This trapped heat warms the planet, making it habitable. However, an increase in the concentration of these gases, primarily due to human activities, enhances this effect, leading to global warming and climate change.
The question asks to identify a popular technique used for forecasting. We need to evaluate each option based on its primary application in statistical and analytical fields.
Correct Option: B) regression analysis
Regression analysis is a fundamental and widely used statistical technique specifically designed for modeling relationships between variables to make predictions or forecasts. It allows us to estimate how a dependent variable changes as one or more independent variables change.
The question asks to identify the country that successfully sent a spacecraft into Mars' orbit on its very first attempt. This requires knowledge of space exploration history, specifically Mars missions by different nations.
India, through its space agency ISRO (Indian Space Research Organisation), launched the Mars Orbiter Mission (MOM), also known as Mangalyaan, on November 5, 2013. The spacecraft successfully entered Mars' orbit on September 24, 2014. This achievement made India the first Asian nation to reach Mars orbit and, more significantly, the first country in the world to do so on its maiden attempt. This was a remarkable feat given the high failure rate of Mars missions globally.
To convert a hexadecimal number to its decimal equivalent, we multiply each digit of the hexadecimal number by \(16\) raised to the power of its position, starting from the rightmost digit with position \(0\).
The calculation is as follows:
\[\begin{aligned} (\text{BE5C})_{16} &= (\text{B} \times 16^3) + (\text{E} \times 16^2) + (5 \times 16^1) + (\text{C} \times 16^0) \ &= (11 \times 16^3) + (14 \times 16^2) + (5 \times 16^1) + (12 \times 16^0) \ &= (11 \times 4096) + (14 \times 256) + (5 \times 16) + (12 \times 1) \ &= 45056 + 3584 + 80 + 12 \ &= 48732 \end{aligned}\]A) 48732 is the correct decimal equivalent of (BE5C)16.
The question asks for the next probable year of visibility for Halley's Comet. This requires knowledge of the comet's orbital period and its last observed appearance.
Correct Option: C) 2061 A.D. is the most probable year for the next visibility of Halley's Comet, based on its orbital period of approximately 75-76 years and its last appearance in 1986. \(1986 + 75 = 2061\).
System analysis is a crucial phase in the System Development Life Cycle (SDLC). It involves understanding the current system, identifying problems, and defining requirements for a new or improved system. The initial step in this process is to get a clear understanding of the project and gather preliminary information.
Correct Option: B) orientation and fact finding. This is the foundational first step where the analyst gets acquainted with the system, its environment, and gathers preliminary information to define the scope and objectives of the analysis.
This problem involves concepts of boats and streams. We need to find the speed of the stream given the total time for a round trip and a relationship between the speed downstream and upstream. We will use variables to represent the speed of the man in still water and the speed of the stream, set up equations based on the given information, and solve for the unknown.
Let the speed of the man in still water be \(x\) kmph and the speed of the stream be \(y\) kmph.
When rowing with the stream (downstream), the effective speed is the sum of the man's speed and the stream's speed:
\[ \text{Speed downstream} = (x + y) \text{ kmph} \]
When rowing against the stream (upstream), the effective speed is the difference between the man's speed and the stream's speed:
\[ \text{Speed upstream} = (x - y) \text{ kmph} \]
The problem states that the man can row 4 km with the stream in the same time as 3 km against the stream. Let this time be \(t\).
Using the formula \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\):
Time taken to row 4 km downstream:
\[ t = \frac{4}{x + y} \]
Time taken to row 3 km upstream:
\[ t = \frac{3}{x - y} \]
Since the times are equal:
\[ \frac{4}{x + y} = \frac{3}{x - y} \]
Cross-multiply to get a relationship between \(x\) and \(y\):
\[ 4(x - y) = 3(x + y) \]
\[ 4x - 4y = 3x + 3y \]
\[ 4x - 3x = 3y + 4y \]
\[ x = 7y \quad \text{(Equation 1)} \]
This means the man's speed in still water is 7 times the speed of the stream.
The man rows to a place 48 km distant and comes back in 7 hours. This means the total time for the round trip (48 km downstream + 48 km upstream) is 7 hours.
Total time = Time downstream + Time upstream
\[ 7 = \frac{48}{x + y} + \frac{48}{x - y} \quad \text{(Equation 2)} \]
Substitute Equation 1 (\(x = 7y\)) into Equation 2:
\[ 7 = \frac{48}{7y + y} + \frac{48}{7y - y} \]
\[ 7 = \frac{48}{8y} + \frac{48}{6y} \]
\[ 7 = \frac{6}{y} + \frac{8}{y} \]
\[ 7 = \frac{6 + 8}{y} \]
\[ 7 = \frac{14}{y} \]
Solve for \(y\):
\[ y = \frac{14}{7} \]
\[ y = 2 \text{ kmph} \]
The rate of the stream is 2 kmph.
C) 2 kmph is the correct answer. The calculation shows that the speed of the stream is 2 kmph.